Common Denominators in I Ching

Every few years I find myself trying to chart the I Ching; trying to find the magic square, knight's tour, strange attractor or mathmatic axiom that will illuminate the structure of the Changes. I've read numerous good treatices towards this end. Govinda presented an elegant diagram that presents the hexagrams as paths rather than as places. Yan and Schonberger relate it to DNA. T.Payne works from D.f.Hook to present it as a family. Hook posed a sequence of reducing the hex.s thru' nuclear trigrams to "bases" of "Ch'ien"(1), "K'un"(2) and Before & After Completion(63)/(64).

Some eight years ago I had charted a sequence of reducing the hex.s thru' the changing and constituting lines. I was curious to see if these ideal changes taken to their final changes would result in "common denominators"; base hex.s as it were. The results for just ruling lines were interesting, but not dramatic- some 10 groups of 3 to 6 hex.s each, but with (2) having 28 hex.s for herself. However, this last time I concentrated on using both ruling AND constituting lines. The constituting lines are those that show the character of the hex....and often occur in the human (2 middle lines) sector. The human factor is as much a force of change as are the laws (or whims) of heaven and earth.[see fig.1a&b]

At any rate, the results of using both ruling and constituting lines WERE dramatic. I charted the groups and who came thru' who to reach the denominators of: (1), (2), (5,11,63), (6,64) and the duo of (49,55). I was struck first by the logic of the groups; the King and his Daughters in one and the Queen and her Sons in another, then a ring and a tree.....then the groups seemed to be courts in the royal palace....the personalities of the different hex.s were related and relating to each other in scripts of action and reaction, stories; classic, tragic, powerful and intriguing. These courts were not the linear mathmatic secret answer I had been looking for, but organic structures. [see fig.2]

is about approaching the powerful: the King to Spiritual power and the people to the King's power. In his right hand is the rod of power(14) Possesion in Great Measure- his manifest of rule; the instrument thru' which he receives the wisdom to be a channel to guide the world. Surrounding the rod are perhaps a group of advisors...his "gentle" (57) daughter is here- poor thing..she gets "work on spoiled" and "gradual developement", but I picture her as a scholar.

At his left hand is his favorite daughter (30); Li- embodiment of fire- as nearly like him as naturally possible. At her left is (58); the young and spoiled one, resentful of having to go thru' (30) to get to her father. If she flanks her sister-(44)); Coming to meet....(bad girl)

Below the King- directly connected to him, but to one else, is the powerful, but vulnerable (54)- must be the concubine. Darkening (36) is injury to the favorite daughter, maybe thru' the power of the small. I can't resist assigning elements to these five groups and this court is Fire: food for spirit.

is about the ties that bind: union and gathering, (v.s.)splitting and return. Her emblem of office seems to be (15); Modesty- her most prolific channel. The aloof son (52) comes in thru' this door. The Caldron ( 1 of 2- man made objects) is on this branch; nourishment of an earthy sort perhaps...so abundent it may spill. Next door is (16); Enthusiasm. Excitable son (51) comes here..along with following and oppression- sounds like the party place. Next door the Fool walks thru' a mirror to become receptive. Her favorite son (29) Abyss is close to hand, dangerous and unconnected to anyone else...lower than the Golden modesty. It is the aloof(52) that marriage may come to. Element: Earth; food for the body.

is about inspiration and creativity.....waiting for and experiencing nourishment and the aftermath. The Well (the 2nd- man made object) is here pushing upward into the ring. I see this as the artist's wing or poet's corner with Grace and Heaven on Earth...Yet in Power of the Great; there's one ruling line in the 4th place(human sector) -a "man's" voice is heard in heaven on earth. The Family power is tamed to enter the ring. Element: Water; food for thought.

is about conflict- avoiding it by increase or biting thru' it...more than one can chew? ...being robbed, opposed, dispersed and stagnated....Perhaps these are merchants. Element: Wood

is about the rich and the poor; Abundance and Revolution. Element: Metal

(c) Randee Z , Tujunga, Ca.,USA. . Jan. of 1999